The deep atmosphere of Venus and the possible role of density-driven separation of CO2 and N2

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The deep atmosphere of Venus and the possible role of density-driven separation of CO2 and N2

Sébastien Lebonnois, Gerald Schubert

To cite this version:

Sébastien Lebonnois, Gerald Schubert. The deep atmosphere of Venus and the possible role of density-

driven separation of CO2 and N2. Nature Geoscience, Nature Publishing Group, 2017, 10 (7), pp.473

- 477. �10.1038/ngeo2971�. �hal-01635402�

The deep atmosphere of Venus and the possible role of density-driven separation of CO ₂ and N ₂

Sebastien Lebonnois,

Gerald Schubert

1

Laboratoire de M´et´eorologie Dynamique (LMD/IPSL),

Sorbonne Universit´es, UPMC Univ Paris 06, ENS, PSL Research University, Ecole Polytechnique, Universit´e Paris Saclay, CNRS, Paris, France

2

Department of Earth, Planet. and Space Sci., UCLA, CA, USA

∗

e-mail: [email protected].

With temperatures around 700 K and pressures of around 75 bar, the deepest

1

12 kilometres of the atmosphere of Venus are so hot and dense that the atmo-

2

sphere behaves like a supercritical fluid. The Soviet VeGa-2 probe descended

3

through the atmosphere in 1985 and obtained the only reliable temperature

4

profile for the deep Venusian atmosphere thus far. In this temperature profile,

5

the atmosphere appears to be highly unstable at altitudes below 7 km, con-

6

trary to expectations. We argue that the VeGa-2 temperature profile could be

7

explained by a change in the atmospheric gas composition, and thus molec-

8

ular mass, with depth. We propose that the deep atmosphere consists of a

9

non-homogeneous layer in which the abundance of N

- the second most abun-

10

dant constituent of the Venusian atmosphere after CO

- gradually decreases

11

to near-zero at the surface. It is difficult to explain a decline in N

towards the

12

surface with known nitrogen sources and sinks for Venus. Instead we suggest,

13

partly based on experiments on supercritical fluids, that density-driven sep-

14

aration of N

from CO

can occur under the high pressures of Venus’s deep

15

atmosphere, possibly by molecular diffusion, or by natural density-driven con-

16

vection. If so, the amount of nitrogen in the atmosphere of Venus is 15% lower

17

than commonly assumed. We suggest that similar density-driven separation

18

could occur in other massive planetary atmospheres.

19

Venus has a massive and scorching atmosphere. With a surface pressure of 92 bars its atmo-

20

sphere is 92 times as massive as Earth’s atmosphere. At the surface of Venus the temperature

21

is 464

C, hot enough to melt lead. Atmospheric density at the surface is about 65 kg m

or

22

6.5% the density of liquid water.

Atmospheric composition is 96.5% CO

and 3.5% N

(by

23

volume).

Minor gases include SO

, Ar, H

O, and CO.

SO

at the level of only 150 ppm is

24

particularly important because of the blanket of sulfuric acid clouds that completely shroud the

25

planet from view.

The clouds effectively reflect the solar radiation incident on Venus resulting

26

in a bond albedo of 0.77, more than double that of the Earth at 0.31. As a consequence more

27

sunlight is absorbed at the surface of Earth than at Venus’ surface even though Venus is 72%

28

nearer to the Sun. The temperature distribution in Venus’ atmosphere is determined in large

29

part by its absorption of sunlight.

Temperature and pressure are so large at Venus’ surface that

30

the atmosphere is a supercritical fluid.

31

In addition to the basic properties above we have detailed knowledge of the atmospheric

32

structure (altitude profiles of temperature and pressure and locations of the clouds) from decades

33

of observation by orbiting spacecraft (Soviet Venera 15 and 16,

U.S. Pioneer Venus Or-

34

biter

and Magellan,

ESA Venus-Express

and the ongoing Japanese Akatsuki), entry

35

probes and landers,

balloons,

and Earth-based telescopes

(Fig. 1). These obser-

36

vations have shown that Venus, like Earth, has a troposphere extending from the surface to the

37

The sulfuric acid clouds extend downward to about 48 km altitude.

Above the clouds are re-

39

gions of the atmosphere analogous to Earth’s mesosphere and thermosphere but our focus here

40

is the atmosphere below the clouds. At cloud heights atmospheric temperature and pressure

41

are similar to those at the Earth’s surface. There is no stratosphere on Venus similar to Earth’s

42

stratosphere that is heated by ozone absorption of solar ultraviolet radiation.

43

The altitude profile of temperature allows identification of stable layers and layers of convec-

44

tive activity. There is a convective region in the clouds between about 50 and 55 km altitude,

45

as experienced by the Soviet VeGa-1 and VeGa-2 balloons that cruised in this layer.

Below

46

this region extending downward to about 32 km altitude the atmosphere is stable. Below this

47

stable layer the atmosphere is well mixed down to an altitude of about 18 km. At even greater

48

depth, the atmosphere is stable again until an altitude of about 7 km. The nature of the lowest

49

7 km of the atmosphere, a layer that contains 37% of the mass of the atmosphere, is at the heart

50

of our discussion.

51

While the exploration of Venus’ atmosphere has been extensive, as discussed above, the

52

deep atmosphere remains a largely unobserved region. It is challenging to obtain data remotely

53

below the thick cloud layer covering the planet. Many probes have been sent to the surface

54

of Venus: the Soviet Venera mission series,

the U.S. Pioneer Venus probes,

and the Soviet

55

VeGa probes.

These probes measured temperature (T ) and pressure (p) during descent, and

56

made measurements of atmospheric composition, showing that the two major constituents were

57

carbon dioxide (CO

, 96.5%) and nitrogen (N

, 3.5%).

Unfortunately, almost no tem-

58

perature data were obtained from the deepest layers of Venus’ atmosphere, since most Venera

59

probe temperature profiles had large uncertainties and all the Pioneer Venus probe temperature

60

experiments stopped functioning at 12 km above the surface.

The Pioneer Venus tempera-

61

ture profiles below 12 km were reconstructed from pressure measurements, extrapolation of

62

T (p) and iterative altitude computation,

and only these reconstructions (prone to significant

63

uncertainties) and the Venera 10 profile

were used to build the Venus International Reference

64

Atmosphere model.

The only available and reliable temperature profile reaching to the surface

65

was acquired by the VeGa-2 probe

(Fig. 2). Measurements were done with two different

66

platinum wires (one bare, one protected in a thin ceramic shield), with a measured accuracy

67

of ±0.5 K from 200 to 800 K. The time constants of the two detectors were 0.1 s and 3 s.

68

The delay of the second detector induced systematic shift between the two measurements, with

69

differences no larger than 2 K down to the surface.

The measured temperature profile fits re-

70

markably well with the Pioneer Venus and VIRA profiles above roughly 15 km altitude.

This

71

illustrates the small temporal and spatial variability of the temperature in the deep atmosphere

72

of Venus, with differences between the different observed profiles smaller than 5 K (and not

73

depending on altitude).

74

Below 7 km, a region where no precise measurements of N

abundance was published,

75

the VeGa-2 temperature profile showed a strongly unstable vertical temperature gradient that

76

has remained unexplained since VeGa-2 landed on Venus on June 15, 1985.

The difference

77

in temperature between the adiabatic profile (neutral stability) and the observed profile is up

78

to roughly 9 K around 7 km. This interface region between the surface and the atmosphere,

79

called the planetary boundary layer (PBL), controls how the angular momentum and energy

80

are exchanged between the two reservoirs. Characterization of the mixing processes occuring

81

in the PBL is crucial to understanding the angular momentum budgets of the atmosphere and

82

solid planet. This is particularly true in the case of Venus, which is characterized by a peculiar

83

atmospheric circulation, the superrotation: the whole atmosphere is rotating much faster than

84

the surface below, with maximum zonal winds reaching more than 100 m/s at the altitude of the

85

cloud top (70 km).

This large zonal rotation of the massive Venus atmosphere makes its atmo-

86

spheric angular momentum a relatively large fraction (1.6×10

) of the angular momentum of

87

the solid body. For Earth this fraction is 2.7×10

. Exchanges of angular momentum between

88

the two reservoirs would lead to changes in the length of day of Venus and zonal wind speeds

89

in the atmosphere.

90

A possible interpretation of this peculiar temperature structure involves unexpected proper-

91

ties of the CO

/N

mixture in high-pressure, high-temperature conditions, which are not well

92

known. This is illustrated by a recent experiment that shows a vertical separation between

93

these two compounds within the fluid phase, a behavior difficult to explain.

Despite a lack

94

of theoretical and experimental constraints, this density-driven separation may be the key to

95

understanding the structure of the deepest layers of Venus’ atmosphere.

96

Stability in the deep atmosphere of Venus

97

The temperature profile close to the surface is a very good indicator of the properties of the PBL.

98

In addition to the static stability, the potential temperature is an efficient variable to analyze the

99

stratification of the atmosphere (Box 1). The vertical profiles of the potential temperature de-

100

rived from the VeGa-2 and Pioneer Venus probes are displayed in Fig. 3. Layers with constant

101

potential temperature are layers where the temperature follows the adiabatic lapse rate, indica-

102

tive of convection or large-scale vertical mixing. Below roughly 7 km, the vertical gradient of

103

the VeGa-2 potential temperature is approximately constant and strongly negative (-1.5K/km),

104

corresponding to a highly unstable situation. Such a profile of potential temperature is never

105

observed on Earth. On Mars, radiative surface heating sometimes drives a very unstable surface

106

layer, yielding highly active convection up to 9 km above surface. In these conditions, the po-

107

tential temperature may display negative gradients over the surface, up to 1 or 2 km altitude.

108

For Venus, this situation is unlikely, as direct heating of the surface is only a small fraction of

109

that of Mars’ surface.

110

However, the VeGa-2 probe potential temperature profile can be understood if the stability of

111

this layer is altered by a vertical gradient in the mean molecular mass (µ), i.e., in the atmospheric

112

gas composition (as detailed in the online Methods section): the assumption that this layer is

113

close to convective instability yields a vertical profile of mean molecular mass which is almost

114

linear with the logarithm of pressure, from 43.44 g/mol above 7 km to 44.0 g/mol at the surface.

115

A density-driven gas separation hypothesis

116

Though a systematic error in the temperature measurements can not be excluded, the fact that

117

this error would have maintained a stable vertical temperature gradient from 7 km altitude to

118

the surface, for both VeGa-2 temperature sensors is unlikely. If this temperature profile is

119

accurate, then it may be neutrally stable with the previously mentioned variation in the mean

120

molecular mass µ. The value obtained in this case for µ at the surface is remarkably close

121

to that of pure CO

, so that an intriguing, but very simple explanation for the vertical profile

122

of µ is a regular decrease in N

mole fraction, from 3.5% above 7 km to almost zero at the

123

surface. Such a composition variation would have a significant impact on the total amount of

124

nitrogen contained in the atmosphere, which would decrease to only 85% of the total amount for

125

a well mixed atmosphere. This could have potential implications for studies that investigate the

126

respective nitrogen inventories of Earth and Venus.

The increase of the mean molecular mass

127

towards the surface might also be consistent with an increase in the abundance of an atmospheric

128

compound heavier than CO

, though this would be an even more puzzling coincidence. For an

129

increase up to the 0.1% level at the surface, the molar mass of the component would need to

130

be of the order of 560 g/mol. A lower molar mass would mean a higher abundance. Solutions

131

could be found, but it seems quite unlikely that the change of composition would be different

132

from the decrease of N

abundance as the surface is approached.

133

Based on this hypothetical interpretation of the VeGa-2 probe temperature profile, the gra-

134

dient in N

abundance obtained in Venus’s deep atmosphere is around 5 ppm/m. In planetary

135

atmospheres, such vertical gradients of composition are usually associated with sources or sinks

136

of the varying compound, such as chemistry, condensation, or surface processes. However, the

137

hypothesis that this nitrogen gradient might be the result of a surface sink faces serious diffi-

138

culties. It would require a constant downward flux of nitrogen, that would need to be sustained

139

over geological times unless a recycling process or an equivalent source could drive nitrogen

140

back into the atmosphere.

141

Another possibility is explored here : this gradient may result from an equilibrium state due

142

to separation of nitrogen from carbon dioxide in the dense conditions of Venus’s deep atmo-

143

sphere. Such a separation of N

and CO

in high-pressure conditions is illustrated by recent ex-

144

periments.

Though the conditions of these experiments are clearly different from conditions

145

in the deep atmosphere of Venus, it demonstrates the impact of high densities on the CO

/N

146

binary mixture. In the first of these experiments,

a mixture of 50% N

/50% CO

(mole frac-

147

tions) was put in an 18-cm high vessel at room temperature for pressures above 100 bars. At

148

p = 100 bars and T = 23

C, the CO

/N

mixture is supercritical, not far above the critical

149

point of the fluid mixture (T

= −9.3

C, p

= 98 bar), and CO

departs slightly from being

150

ideal. Using the equations of state for pure CO

and N

,

CO

partial pressure is 44 bars,

151

CO

density is 101 kg/m

and total density in the vessel is around 165 kg/m

, to be compared

152

with the densities in the deep Venusian atmosphere: 40 to 70 kg/m

for pressures higher than

153

50 bars. In these experimental conditions, N

and CO

were observed to separate significantly

154

along the vertical dimension, N

reaching over 70% mole fraction at the top of the vessel, while

155

CO

reached almost 90% at the bottom.

Over the 18 cm of the experimental vessel, this sep-

156

aration is extreme, with an average gradient of 3 to 4%/cm. In Venus’s deep atmosphere, the

157

5 ppm/m gradient in N

abundance appears much smaller in comparison.

158

The molecular diffusion in this binary gas mixture includes three terms: one due to the

159

compositional gradient, one due to the temperature gradient, and one due to the pressure gra-

160

dient.

The amplitude of this pressure term is controlled by the barodiffusion coefficient k

.

161

Molecular diffusion in an ideal gas mixture increases as the pressure decreases towards higher

162

altitudes, the expression of k

is known for an ideal binary gas mixture, and turbulent diffusion

163

in usual atmospheric conditions is strong enough to homogenize atmospheric composition up to

164

the homopause. At this level, molecular diffusion dominates and the barodiffusion induces mass

165

separation of the different compounds. Could high-pressure conditions and departure from the

166

ideal gas law induce strongly non-linear behavior of the barodiffusion coefficient ? For such

167

a gradient to be maintained in the near-surface layer of Venus’s atmosphere against large-scale

168

and turbulent mixing, the barodiffusion coefficient k

would need to be several orders of mag-

169

nitude larger than for an ideal gas in the same conditions, which may seem highly unlikely. It

170

is also the case for the previously detailed experiment.

Unfortunately, no measured or theo-

171

retical values are yet available for k

, neither for the experimental set-up

nor for Venus’s deep

172

atmospheric conditions. In the experiments,

natural density-driven convection is mentioned

173

as a possible driver, inducing transport of nitrogen-rich lighter parcels upward while CO

-rich

174

heavier parcels would move downward. Additional experimental and theoretical studies are

175

clearly needed to investigate this possibility and to solve this puzzle.

176

Dynamics of the deep atmosphere of Venus

177

To better understand the dynamical state of the different atmospheric layers, as well as the be-

178

havior of the PBL near the surface of Venus, the atmospheric circulation was explored using the

179

Laboratoire de Meteorologie Dynamique (LMD) Venus General Circulation Model (GCM).

180

The variation of the mean molecular mass with pressure in the deep atmosphere was imple-

181

mented in the computation of the potential temperature within the GCM, though this modi-

182

fication only slightly affects the dynamical state ot the deepest layers. Fitting the observed

183

temperature structure in detail with a radiative transfer model is challenging, because of the

184

sensitivity of the temperature profile to many parameters that are not well known.

However,

185

with a fine tuning of these parameters (detailed in the online Methods section), the GCM is able

186

to reproduce the vertical structure of the potential temperature. Therefore, the mean meridional

187

circulation and the turbulent activity diagnosed by the GCM (Fig. 4) can be used to evaluate the

188

dynamical conditions within the atmosphere, including the deepest layer discussed here, despite

189

the large difficulty to get observational constraints for this region.

190

The deepest layer (below 8 km) is close to neutral stability. In the simulation, it is slightly

191

turbulent only near its top, and near the surface with a diurnal convective layer that reaches 1

192

to 2 km above the surface around noon local time. This result of the GCM radiative transfer

193

is obtained both when taking into account the composition variation and when composition is

194

uniform. The mean meridional circulation participates in the mixing of the energy through a

195

surface Hadley-type cell roughly 7-km thick. This is similar to the 2-km thick seasonal PBL

196

observed on Titan by the Huygens probe, associated with the mixing by the deepest mean

197

meridional circulation cells.

The hypothetical separation of N

and CO

that would explain the

198

VeGa-2 potential temperature profile in the deepest layer needs to occur on timescales shorter

199

than the dynamical overturning of this surface cell (τ

= L/v, where L ∼ 10

km is the

200

horizontal size of the cell and v ∼ 0.05 m/s is the mean meridional wind near the surface,

201

yielding τ

∼ 2×10

s, or 20 Vd) in order to maintain this vertical gradient in the atmospheric

202

composition, while the layer is close to convective instability. The simulation confirms the very

203

small spatial and temporal variations of the temperature profile, with a diurnal cycle only active

204

near the surface.

205

Dense gas separation at Venus and beyond

206

The unexplained behavior of the CO

/N

mixture in the temperature and pressure conditions

207

of the deep atmosphere of Venus needs to be confirmed. First, it illustrates how important it

208

is to go back to Venus to make additional in-situ measurements down to the surface. Second,

209

further studies are needed, both theoretical and experimental. The compositional gradient de-

210

duced from our interpretation of the VeGa-2 profile (5 ppm/m) could be measured in a large

211

experimental tank where Venus’ atmospheric conditions can be reproduced. Such a result could

212

trigger interest for theoretical and experimental studies dedicated to other binary mixtures, that

213

could be relevant for the high-pressure atmospheres of giant planets of our own solar system, or

214

for extra-solar planets.

215

216

Figure 1 | Vertical structure of the atmosphere of Venus. Vertical profiles, as a function of

217

altitude and pressure, of the temperature, density and static stability (i.e., the difference between

218

the vertical gradient of temperature and the adiabatic lapse rate), from the Venus International

219

Reference Atmosphere model.

Cloud layers are also indicated.

220

221

Figure 2 | The VeGa-2 spacecraft. Model of the VeGa spacecraft, with the lander visible in the

222

top spherical shell (Lavochkin Museum, near Moscow). Image credits: Lavochkin Association.

223

224

Figure 3 | Vertical profile of potential temperature θ computed from temperatures mea-

225

sured by VeGa-2. Potential temperature is computed using Eq. S10 in the online Methods.

226

VeGa-2 profile shows the convective layer present in the middle and lower clouds (48-56 km al-

227

titude), observed in all in-situ and radio-occultation datasets,

as well as a deep-atmosphere

228

mixed layer (17-32 km altitude), consistent with the Venus International Reference Atmosphere

229

(VIRA) model

and the Pioneer Venus Sounder, Day and Night probes.

The highly unstable

230

7-km thick surface layer is also highlighted (µ is the mean molecular mass of the atmosphere).

231

232

Figure 4 | Meridional distributions of the turbulent mixing coefficient and averaged stream

233

function. The diurnal and zonal average of the turbulent mixing coefficient K

diagnosed in

234

the GCM is shown with colors (unit is m

/s), showing convective regions, while the mean

235

meridional circulation is illustrated by the averaged stream function with the white contours

236

(unit is 10

kg/s). The amplitude of K

reaches more than 10 m

/s in the cloud turbulent layer

237

(48-57 km).

238

Box 1

239

The stability of an atmospheric region is assessed by moving adiabatically an air parcel along the

240

vertical. For an ideal gas, its temperature follows the adiabatic lapse rate

adiab

= Γ = −

p

,

241

where g is the gravity and c

is the specific heat capacity at constant pressure. In a well mixed

242

atmosphere (constant molecular mass µ), if the parcel rises to a colder environment (or sinks

243

to a warmer environment), it will continue to rise (or sink), becoming buoyant and triggering

244

convective activity. This corresponds to a vertical temperature gradient lower than the adiabatic

245

lapse rate. The stability can then be assessed with the static stability: S =

− Γ: when S is

246

positive, the atmosphere is stable, but when S is negative, convective activity will mix energy

247

and modify the temperature profile until S = 0.

248

The potential temperature θ is defined as the temperature that an air parcel would get after

249

undergoing an adiabatic displacement from its position (T, p) to a reference pressure p

. The

250

static stability S is equivalent to the vertical gradient of the potential temperature,

.

251

When the mean molecular mass is not constant with altitude, to define the buoyancy of a

252

given parcel, the relevant variable is the potential density ρ

, defined as the density a parcel with

253

the density ρ(µ, T, p) would have when displaced adiabatically (and with constant composition)

254

to the reference pressure p

, ρ

(µ, θ, p

). In the case of the deep atmosphere of Venus, the

255

stability criterion can be reduced to the usual criterion, but applied to the modified potential

256

temperature θ

= θ(µ

/µ), with µ

= 43.44 g/mol a reference value corresponding to CO

257

mixed with 3.5% of N

:

≥ 0.

258

Additional details may be found in the online Methods section.

259

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32. Read, P. L. et al. Global energy budgets and ‘Trenberth diagrams’ for the climates of

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terrestrial and gas giant planets. Quater. J. R. Met. Soc. 142, 703–720 (2016).

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355

Acknowledgements

356

The authors thank Ludmila Zasova for providing the VeGa-2 probe temperature profile, and

357

Josette Bellan for mentioning barodiffusion and useful discussion on this phenomenon. S.L.

358

acknowledges the support of the Centre National d’Etudes Spatiales. G.S. acknowledges the

359

support of the Keck Institute for Space Studies under the project ”Techniques and technologies

360

for investigating the interior structure of Venus”.

361

Methods

362

Stability and potential temperature

363

The stability of an air parcel undergoing an adiabatic displacement in situations where µ and/or

364

c

may depend on altitude, pressure or temperature is detailed in the following study. The

365

notations used are as follows: R is the universal gas constant (R=8.3144621 J mol

K

), µ is

366

the mean molecular mass, p is the pressure, ρ is the density, v = 1/ρ is the specific volume, T

367

is the temperature, c

and c

are the specific heat capacities at constant pressure and constant

368

volume, λ = c

/c

and κ = R/(µc

).

369

Initial equations. The basic equations for this study are:

370

- the specific heat relations

371

(Eq. S1)

372

dU = c

dT (Eq. S2)

373

R

µ = c

− c

which yields

374

κ = 1 − 1 λ

- the first law of thermodynamics for adiabatic displacement

375

(Eq. S3)

376

dU = −pdv - the equation of state for an ideal gas

377

(Eq. S4)

378

ρ = µp

RT

Note that in the case of the deep atmosphere of Venus, the ideal gas law is only an approxi-

379

mation, but with an error on density less than 0.8% (Table S1).

380

- the hydrostatic balance

381

(Eq. S5)

382

dp = −ρgdz

When µ is constant in the atmosphere. In the cases where µ is constant in the atmosphere,

383

Eq. S4 can be written as:

384

pv = R µ T Differentiating this equation yields

385

(Eq. S6)

386

pdv + vdp = R µ dT From Eqs. S1 and S3, we get

387

pdv = −c

dT Together with Eq. S2, Eq. S6 becomes

388

vdp = c

dT

Using Eq. S4 again, this yields

389

(Eq. S7)

390

R µ

dp

p = c

dT T

The potential temperature θ is defined as the temperature that an air parcel would get after

391

undergoing an adiabatic displacement to a reference pressure p

. Its expression is obtained

392

by integrating this adiabatic displacement from (T, p) to (θ, p

). When c

is constant, Eq. S7

393

yields the usual expression

394

(Eq. S8)

395

θ = T p

p

!κ

When c

depends on the temperature, the integration is not direct. Using the expression

396

(Eq. S9)

397

c

= c

T T

ν

(with c

=1000 J/kg/K, T

= 460 K and ν = 0.35 for Venus’ atmosphere),

it can be

398

demonstrated

that the new expression for θ is:

399

(Eq. S10)

400

θ

= T

+ νT

ln p

p

!κ0

with κ

= R/(µc

).

401

Using Eqs. S4, S5 and S7 yields

402

− gdz

T = c

dT T

which gives the adiabatic lapse rate (valid even for variable c

)

403

(Eq. S11)

404

dT dz

!

adiab

= Γ = − g c

When µ depends on altitude, pressure or temperature. The stability criterion is established

405

as follows.

Consider a parcel that is displaced adiabatically on an elemental distance dz, q∗

406

refers to the variable q in the parcel.

407

Eq. S4 can be written as

408

p∗µ∗ = ρ∗RT ∗

Taking the logarithm then differentiating along the vertical axis (µ∗ is constant because the

409

composition of the parcel does not change) yields

410

1 p∗

dp∗

dz = 1 ρ∗

dρ∗

dz + 1 T ∗

dT ∗

dz

Using Eq. S7 applied to the parcel and p = p∗ yields

411

(Eq. S12)

412

1 ρ∗

dρ∗

dz = 1 p

dp

dz (1 − κ∗) with κ∗ = R/(µ∗c

).

413

For the background gas, Eq. S4 can be written as:

414

ρ = µp RT

Taking the logarithm then differentiating along the vertical axis yields

415

(Eq. S13)

416

1 ρ

dρ dz = 1

µ dµ dz + 1

p dp dz − 1

T dT

dz The stability criterion is

417

(Eq. S14)

418

1 ρ∗

dρ∗

dz > 1 ρ

dρ dz Eqs. S12 and S13 yield

419

(Eq. S15)

420

1 µ

dµ dz − 1

T dT

dz + κ∗

p dp dz < 0

Applying this stability criterion, the adiabatic lapse rate is obtained when neutral for stabil-

421

ity:

422

(Eq. S16)

423

1 µ

dµ dz − 1

T dT

dz + κ∗

p dp dz = 0

Using Eqs. S4, S5 and the fact that κ/κ∗ tends to 1 for an elemental displacement, this can

424

be written as

425

(Eq. S17)

426

dT

= Γ = T dµ

− g

which is valid even for variable c

.

427

To define the buoyancy of a given parcel, the relevant variable is the potential density ρ

,

428

defined as the density a parcel with the density ρ(µ, T, p) would have when displaced adiabat-

429

ically (and with constant composition) to the reference pressure p

, ρ

(µ, θ, p

). Using the

430

ideal gas law (Eq. S4), the potential density is

431

(Eq. S18)

432

ρ

= µp

Rθ = µ

p

Rθ

with the modified potential temperature θ

defined by

433

(Eq. S19)

434

θ

= θ(µ

/µ)

Due to the variation of µ with altitude and the dependence of θ on µ, it is not correct to

435

reduce the stability criterion (Eq. S16) to the usual criterion, i.e., the direct comparison of the

436

potential density between two atmospheric levels.

437

(Eq. S20)

438

1 ρ

dρ

dz = 1

µ dµ dz − 1

θ

∂θ

∂z

!

µ

− 1 θ

∂θ

∂µ

!

z

dµ dz For an elemental displacement, the definition of θ yields

439

(Eq. S21)

440

1 θ

∂θ

∂z

!

µ

= 1 T

dT dz − κ∗

p dp dz which can be inserted in Eq. S20 to give

441

(Eq. S22)

442

1 ρ

dρ

dz = 1

µ dµ dz − 1

T dT

dz + κ∗

p dp dz − 1

θ

∂θ

∂µ

!

z

dµ dz

Eq. S22 shows that dρ

/dz = 0 (or dθ

/dz = 0) is not equivalent to the stability criterion

443

(Eq. S16), unless the last term of the right side is negligible against the first.

444

However, in the case of the deep atmosphere of Venus, the vertical profile of θ(µ) is very

445

close (difference less than 0.15 K everywhere) to the profile of θ(µ

), with µ

= 43.44 g/mol

446

a reference value corresponding to CO

mixed with 3.5% of N

. This yields (µ/θ)(∂θ/∂µ) ∼

447

(43.44/735) × (0.15/0.56) ∼ 0.016, much smaller than 1. It is therefore a good approximation

448

to consider that the definition of the potential temperature θ is not dependent on the initial mean

449

molecular mass of the air parcel, i.e., ∂θ/∂µ = 0 at any given level. In this case, the stability

450

criterion is equivalent to the usual criterion applied to the modified potential temperature θ

:

451

(Eq. S23)

452

1 θ

dθ

dz = 0.

Radiative transfer details

453

In the GCM used for our study, the temperature structure is modeled using a full radiative

454

transfer model. In the infrared range, net exchange rate (NER) formalism is used

based

455

on up-to-date gas opacities including collision-induced absorption from CO

dimers

, and the

456

most recent cloud model deduced from Venus-Express datasets

. In the solar range, vertical

457

profiles of the solar fluxes computed using this new cloud model are used, depending on lati-

458

tude and solar zenith angle

. As discussed in a recent work

extinction coefficients below the

459

clouds in windows located between 3 and 7 microns play a key role in shaping the deep atmo-

460

sphere temperature profile. The solar heating profile below the clouds is also crucial, though it

461

is poorly constrained by available data.

462

Globally averaged 1-dimensional simulations were performed to assess the sensitivity to

463

crucial hypotheses in the radiative transfer calculation. Different solar heating rate models were

464

used

(Fig. S1a). The composition of the lower haze particles, located between the cloud

465

base (48 km) and 30 km and observed by the probe nephelometers

, is not established, so their

466

optical properties are not well constrained. The absorption of the solar flux in this region is

467

therefore subject to uncertainty. An increased solar absorption (by a factor 3) in this region in

468

the H15 profile

(Fig. S1) provides the best fit to the VIRA and Vega-2 temperature profiles.

469

In the infrared, some additional extinction is needed below the clouds in the 3 to 7 microns

470

wavelength range to fit the temperature profile in the stable region below the clouds

. The

471

lower haze, which is not taken into account in the reference NER computations, can contribute

472

to this small additional continuum. The impact of several hypotheses on this additional opacity

473

is illustrated in Fig. S1b. The best fit to the VIRA and Vega-2 temperature profiles is obtained

474

with an additional extinction of 1.3 ×10

cm

amagat

in the lower haze region (30-48 km),

475

and of 4 × 10

cm

amagat

in the region between 30 and 16 km, where a transition from

476

instability to stability against convection is observed in the Vega-2 profile, but also in the Pioneer

477

Venus Sounder, Day and Night probes at similar altitudes (15 to 20 km)

.

478

References

479

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506

Data and code availability

507

The VeGa-2 temperature profile was provided kindly provided by Ludmila Zasova. It is avail-

508

able from the corresponding author upon request.

509

The LMD Venus GCM used in this study is developed in the corresponding author’s team.

510

Author contributions

512

Both authors contributed equally to the manuscript.

513

Additional information

514

Methods section and Supplementary Information are available in the online version of the paper.

515

Correspondence and requests for materials should be addressed to S.L.

516

Competing financial interests

517

The authors declare no competing financial interests.

518